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Q.

The marks of some students were listed out of 75.The SD of marks was found to be 9. Subsequently the marks were raised to a maximum of 100 and variance of new marks was calculated. The new variance is

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a

81

b

122

c

144

d

None of these

answer is C.

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Detailed Solution

Given, $σ$ =9
Let a student obtains x marks out of 75. Then, his marks out of

100 are $\frac{4 x}{3}$ .Each observation multiple by $\frac{4}{3}$

Now, $SD, σ = \frac{4}{3} \times 9 = 12$

Hence, variance is $σ^{2} = 144$

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The marks of some students were listed out of 75.The SD of marks was found to be 9. Subsequently the marks were raised to a maximum of 100 and variance of new marks was calculated. The new variance is